General Equilibrium and Market Efficiency. Production Economy. Pareto Efficiency. An allocation of goods in an economy is Pareto efficient if there is no other allocation that will make at least one individual in the economy better off without worsening the well-being of the others.

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An allocation of goods in an economy is Pareto efficient if there is no other allocation that will make at least one individual in the economy better off without worsening the well-being of the others.

Assume that Ann’s and Bill’s preferences are (strictly) monotonic and convex

Then in a Pareto optimal allocation the marginal rates of substitution between the two goods (clothing and food) of Ann and Bill should be equal.

Assume Ann is ready to

exchange at most 5 units

of food for 1 unit of clothing,

but Bill’s MRS between

food and clothing is 3

Then a benevolent planner can offer to take 4 units of food from Ann and give it to Bill in exchange for 1 unit of clothing. Both will agree, as the will be happier under the new allocation. Thus, the initial allocation of final goods was not Pareto optimal

The market value produced by the last unit of input (capital, labor) should equal to its rental price in production of food

The same is true for the market value of inputs in production of clothing

Thus, the market value produced by the last unit of capital is the same in both activities. The same is true for labor. The market value of the last unit of capital is its marginal product times the price of output. Therefore,